residual stresses at the stem–cement interface of an idealized cemented hip stem

4
Journal of Biomechanics 35 (2002) 849–852 Technical note Residual stresses at the stem–cement interface of an idealized cemented hip stem N. Nu * no a, *, G. Avanzolini b a D ! epartement de g ! enie m! ecanique, ! Ecole de technologie sup ! erieure, Universit ! e du Qu ! ebec, 1100 rue Notre-Dame O., Montr ! eal, Qu ! e., Canada H3C 1K3 b DEIS, Faculty of Engineering, University of Bologna, viale Risorgimento 2, 40136 Bologna, Italy Accepted 5 February 2002 Abstract During the operation of total hip arthroplasty, when the cement polymerizes between the stem implant and the bone, residual stresses are generated in the cement. The purpose of this study was to determine whether including residual stresses at the stem– cement interface of cemented hip implants affected the cement stress distributions due to externally applied loads. An idealized cemented hip implant subjected to bending was numerically investigated for an early post-operative situation. The finite element analysis was three-dimensional and used non-linear contact elements to represent the debonded stem–cement interface. The results showed that the inclusion of the residual stresses at the interface had up to a 4-fold increase in the von Mises cement stresses compared to the case without residual stresses. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Residual stresses; Stem–cement interface; Cemented hip implant; FEA 1. Introduction One of the main concerns in the success of long-term survival of total hip arthroplasty (THA) is the attach- ment of the prosthesis to the bone. Implant loosening of cemented hip implants is a major cause of late failure of the arthroplasty. It is believed that separation of the stem–cement interface and fractures in the cement may initiate the initial loss of fixation of the implant (Harrigan and Harris, 1991; Jasty et al., 1991). A better knowledge of the load transfer across the stem–cement interface would help in understanding better the mechanism leading to the implant failure. During the operation of THA, when the cement polymerizes around the stem implant, residual stresses are generated in the bulk cement; in particular, normal stresses at the stem–cement interface are developed resulting in a press-fit problem. At the end of the process, when bone cement polymerizes in contact with cortical bone, which has impermeable surfaces, the residual radial stresses always remain compressive at the stem–cement interface due to the cement expansion (Ahmed et al., 1982). Mann et al. (1991) concluded that the behavior of push-through-stem tests and the simulated finite element (FE) model gave the best agreement when friction as well as residual stresses were included in the analysis. In their study, compressive residual radial stresses of 3 MPa were simulated, similar to 2.5 MPa residual stresses found from a thermoelastic analysis by Ahmed et al. (1982). Similar results were obtained by Huiskes (1980). In numerical analyses of hip implants, although the coefficient of friction is usually incorporated, the residual stresses generated due to cement curing are not included (e.g., Lu and McKellop, 1997; Norman et al., 1996). The purpose of this study was to determine whether including residual stresses at the stem–cement interface of cemented hip implants affected the cement stress distributions due to externally applied loads. An idealized cemented hip implant subjected to bending was numerically investigated for an early post-operative situation. The interface characteristics of the debonded stem–cement interface included the residual stresses due to cement curing and Coulomb friction behavior at the interface for a satin finished or polished stem surface. *Corresponding author. Tel.: +1-514-396-8604; fax: +1-514-396- 8530. E-mail address: [email protected] (N. Nu * no). 0021-9290/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII:S0021-9290(02)00026-X

Upload: n-nuno

Post on 02-Jul-2016

219 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Residual stresses at the stem–cement interface of an idealized cemented hip stem

Journal of Biomechanics 35 (2002) 849–852

Technical note

Residual stresses at the stem–cement interface of an idealizedcemented hip stem

N. Nu *noa,*, G. Avanzolinib

aD!epartement de g!enie m!ecanique, !Ecole de technologie sup!erieure, Universit!e du Qu!ebec, 1100 rue Notre-Dame O., Montr!eal, Qu!e.,

Canada H3C 1K3bDEIS, Faculty of Engineering, University of Bologna, viale Risorgimento 2, 40136 Bologna, Italy

Accepted 5 February 2002

Abstract

During the operation of total hip arthroplasty, when the cement polymerizes between the stem implant and the bone, residual

stresses are generated in the cement. The purpose of this study was to determine whether including residual stresses at the stem–

cement interface of cemented hip implants affected the cement stress distributions due to externally applied loads. An idealized

cemented hip implant subjected to bending was numerically investigated for an early post-operative situation. The finite element

analysis was three-dimensional and used non-linear contact elements to represent the debonded stem–cement interface. The results

showed that the inclusion of the residual stresses at the interface had up to a 4-fold increase in the von Mises cement stresses

compared to the case without residual stresses. r 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Residual stresses; Stem–cement interface; Cemented hip implant; FEA

1. Introduction

One of the main concerns in the success of long-termsurvival of total hip arthroplasty (THA) is the attach-ment of the prosthesis to the bone. Implant loosening ofcemented hip implants is a major cause of late failure ofthe arthroplasty. It is believed that separation of thestem–cement interface and fractures in the cement mayinitiate the initial loss of fixation of the implant(Harrigan and Harris, 1991; Jasty et al., 1991). A betterknowledge of the load transfer across the stem–cementinterface would help in understanding better themechanism leading to the implant failure.During the operation of THA, when the cement

polymerizes around the stem implant, residual stressesare generated in the bulk cement; in particular, normalstresses at the stem–cement interface are developedresulting in a press-fit problem. At the end of theprocess, when bone cement polymerizes in contact withcortical bone, which has impermeable surfaces, theresidual radial stresses always remain compressive at the

stem–cement interface due to the cement expansion(Ahmed et al., 1982). Mann et al. (1991) concluded thatthe behavior of push-through-stem tests and thesimulated finite element (FE) model gave the bestagreement when friction as well as residual stresses wereincluded in the analysis. In their study, compressiveresidual radial stresses of 3MPa were simulated, similarto 2.5MPa residual stresses found from a thermoelasticanalysis by Ahmed et al. (1982). Similar results wereobtained by Huiskes (1980). In numerical analyses ofhip implants, although the coefficient of friction isusually incorporated, the residual stresses generated dueto cement curing are not included (e.g., Lu andMcKellop, 1997; Norman et al., 1996).The purpose of this study was to determine

whether including residual stresses at the stem–cementinterface of cemented hip implants affected the cementstress distributions due to externally applied loads.An idealized cemented hip implant subjected tobending was numerically investigated for an earlypost-operative situation. The interface characteristicsof the debonded stem–cement interface included theresidual stresses due to cement curing and Coulombfriction behavior at the interface for a satin finished orpolished stem surface.

*Corresponding author. Tel.: +1-514-396-8604; fax: +1-514-396-

8530.

E-mail address: [email protected] (N. Nu *no).

0021-9290/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 0 2 1 - 9 2 9 0 ( 0 2 ) 0 0 0 2 6 - X

Page 2: Residual stresses at the stem–cement interface of an idealized cemented hip stem

2. Finite element analysis

The geometry of the idealized cylindrical cementedhip stem surrounded by bone, shown in Fig. 1, is similarto the one used by Huiskes (1980). In the FE model, thestem–cement interface was debonded, while the cement–bone interface was bonded since retrieved femoralcomponents have shown that this interface is well fixed(Jasty et al., 1991). All the materials were assumed to belinearly isotropic and homogeneous. The Ti-6Al-4Vstem had Young’s modulus E ¼ 110000MPa and aPoisson ratio n ¼ 0:3; the PMMA cement mantle hadE ¼ 2700MPa and n ¼ 0:35; the cortical bone hadE ¼ 15500MPa and n ¼ 0:28: The distal ends of thecement mantle and the bone were completely fixed.The three-dimensional FE model was solved using the

commercial FE package Ansys 5.4 (Kohnke, 1997).Using symmetry, half of the system consisting of morethan 4300 elements was modeled. The Ti-6Al-4V stem,PMMA mantle and bone were modeled with solidelements Solid45, defined by 8 nodes each having 3degrees of freedom. The cement–bone interface wasassumed rigidly fixed, while the stem–cement interfaceconsisted of 294 non-linear contact elements Contac52,3-D node-to-node elements, using elastic Coulombfriction behavior that allows both sticking and slidingconditions. A coefficient of friction of 0.2 at the stem–cement interface was used; the coefficient of frictiondetermined in a recent experimental study (Nu *no et al.,2002) varied between 0.17 and 0.32 for polished or satinfinish of the stem surface.

The compressive residual radial stresses due to cementcuring at the stem–cement interface were simulated by apress-fit effect: an interference of 5 mm was assigned tothe contact elements corresponding to radial residualstresses of approximately 2.4MPa. This order ofmagnitude for the residual stresses was obtainednumerically by Ahmed et al. (1982) and experimentallyby Nu *no and Cristofolini (2001). A transverse load of600N for the full model was applied on the lateral sideof the stem at 4mm to the right of the proximal end(Fig. 1), assuming the entire body weight to be appliedto one hip only. The femur is primarily loaded inbending (Rohlmann et al., 1983). Another analysis wasperformed for combined loading where both axial andtransverse loads of 600N were considered. The analysisshowed that the axial compression had a small effectcompared to bending; this is to be expected since thestem geometry is slender. The FE analysis determinedthe cement stress distributions; the equivalent vonMises, radial and hoop stresses at the stem–cementinterface are reported in the Section 3.

3. Results

Table 1 summarizes the peak cement stresses at thestem–cement interface of the hip implant subjected tobending by discarding the peak stresses that occurred atthe proximal or distal ends due to the abrupt change ofgeometry. Fig. 2 shows the von Mises cement stresses atthe interface as a function of the axial co-ordinate on the

Fig. 1. Three-dimensional FEM mesh of the cemented hip stem analyzed. All dimensions are in mm.

N. Nu *no, G. Avanzolini / Journal of Biomechanics 35 (2002) 849–852850

Page 3: Residual stresses at the stem–cement interface of an idealized cemented hip stem

lateral side in tension. A 4-fold increase was observed inthe von Mises stresses including the residual stressescompared to the case with no residual stresses.The radial and hoop stresses are also plotted as a

function of the axial co-ordinate (Figs. 3 and 4) toobserve the tensile and compressive stresses along theradial and circumferential directions of the cementmantle, respectively. Zero radial stresses indicated apossible gap at the interface, i.e. the separation of the

surfaces where the load cannot be transferred; lowtensile stresses are due to interpolation errors. In fact, inpure bending, one can assume that compressive radialstresses indicate where the load is being transferred fromthe stem to the cement mantle. On the medial side, mostof the load was transferred at the proximal end. On thelateral side, a portion of the load was transferred at thedistal end; however, the central part also had afundamental role (Fig. 3).

4. Discussion

An idealized geometry was deliberately selected toassess whether including the residual stresses affectedthe load transfer for an early post-operative situation.The effect of the residual stresses shown on a simplemodel can be more effective than that in a complex,more realistic one.In the FE model, residual stresses can be generated

by: (i) interference fit, as in the present study, and (ii)thermal expansion. A thermal expansion of the cementwould have generated larger residual axial stresses thanthose found from this study using an interference fit.However, since the axial direction was unconstrained,

Table 1

Peak stress components in the cement mantle for the medial and lateral sides in the proximal or distal sections of the stem with or without the

inclusion of the residual radial stresses at the interface

Von Mises (MPa) Hoop (MPa) Radial (MPa)

Proximal Distal Proximal Distal Proximal Distal

Medial No residual — 0.89 �0.15 — — �0.70Medial Residual — 3.68 1.49 — — �2.98Lateral No residual 4.40 0.87 �0.41 0.10 �4.53 0.00

Lateral Residual 5.78 3.45 0.78 1.34 �5.33 �2.24

Negative sign refers to compressive stresses.

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80

Axial position, z (mm)

von

Mis

es s

tres

ses

(MP

a)

No residual stresses

With residual stresses

Fig. 2. Von Mises stresses in the cement mantle at the interface on the

lateral side without and with residual radial stresses versus the axial co-

ordinate z.

-7.0

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

0 10 20 30 40 50 60 70 80

Axial position, z (mm)

Rad

ial s

tres

ses

(M

Pa)

No residual stresses

With residual stresses

Fig. 3. Radial stresses in the cement mantle at the interface on the

lateral side for without and with residual radial stresses versus the axial

co-ordinate z.

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0 10 20 30 40 50 60 70 80

Axial position, z (mm)

Ho

op

str

esse

s (M

Pa)

No residual stresses

With residual stresses

Fig. 4. Hoop stresses in the cement mantle at the interface on the

lateral side for without and with residual radial stresses versus the axial

co-ordinate z.

N. Nu *no, G. Avanzolini / Journal of Biomechanics 35 (2002) 849–852 851

Page 4: Residual stresses at the stem–cement interface of an idealized cemented hip stem

the cement was free to expand axially, and presumablythe stresses would not be large. It must be noted thatduring the operation of THA axial expansion is allowed.The PMMA was assumed linearly elastic in the FE

model. It is known that cement creep decreases thecement stresses (e.g., Huiskes, 1980; Norman et al.,1996; Lu and McKellop, 1997; Verdonschot andHuiskes, 1996). In particular, Lu and McKellop (1997)showed that creep is much smaller if bone is includedthan for unconstrained specimens. The cement stressescomputed in the present study could be lower due tocreep, but the residual stresses caused by cement curingare not expected to disappear at least in the early post-operative period. However, experiments should beconducted to give qualitative answers to this controver-sial issue.The maximum von Mises stresses clearly showed that

the magnitude of the residual stresses affected thecement stress distributions at the stem–cement interface.

5. Conclusions

The results of this study showed that the inclusion ofthe residual stresses affected the cement stress distribu-tions at the stem–cement interface. The trends of thecement stress distributions are similar without and withresidual stresses modeled at the stem–cement interface,however, the magnitudes differ. The results showed thatthe peak cement stresses are underestimated when theFE analysis does not include the residual stresses due tocement curing. Since there is no chemical bond at theinterface between the stem and cement, the interfaceresistance depends on friction, thus, radial compressivestresses developed by cement curing play a direct role.The residual stress magnitudes may vary with differentimplant designs, and although creep will decrease thesestresses they are not expected to disappear in an earlypost-operative situation. The load transferred from thestem to the bone occurs primarily across the interfaces;consequently, accurately modeling the interface essentialin predicting the load transfer (Joshi et al., 2000). Inorder to better determine the magnitude of the residualstresses more experimental results are needed; never-theless, to model accurately the stem–cement interface,

residual stresses due to cement curing should beincluded in FE analyses.

References

Ahmed, A.M., Nair, R., Burke, D.L., Miller, J., 1982. Transient and

residual stresses and displacements in self-curing bone cement—

Part 2: thermoelastic analysis of the stem fixation system. ASME

Journal of Biomechanical Engineering 104, 28–37.

Harrigan, T.P., Harris, W.H., 1991. A three-dimensional non-linear

finite element study of the effect of cement-prosthesis debonding in

cemented femoral total hip components. Journal of Biomechanics

24, 1047–1058.

Huiskes, R., 1980. Some fundamental aspects of human joint

replacement. Acta Orthopaedica Scandinavica Supplement 185,

208.

Jasty, M., Maloney, W.J., Bragdon, C.R., O’Connor, D., Haire, T.,

Harris, W.H., 1991. The initiation of failure in cemented femoral

components of hip arthroplasties. Journal of Bone Joint Surgery

73B, 551–558.

Joshi, M.G., Santare, M.H., Advani, S.G., 2000. Survey of stress

analyses of the femoral hip prosthesis. ASME Applied Mechanics

Reviews 53, 1–18.

Kohnke, P. (Ed.), Ansys Theory Reference Manual, Release 5.4. Ansys

Inc, 1997.

Lu, Z., McKellop, H., 1997. Effects of cement creep on stem

subsidence and stresses in the cement mantle of a total hip

replacement. Journal of Biomedical Materials Research 34,

221–226.

Mann, K.A., Bartel, D.L., Wright, T.M., Ingraffea, A.R., 1991.

Mechanical characteristics of the stem–cement interface. Journal of

Orthopaedic Research 9, 798–808.

Norman, T.L., Saligrama, V.C., Hustosky, K.T., Gruen, T.A., Blaha,

J.D., 1996. Axisymmetric finite element analysis of a debonded

total hip stem with an unsupported distal tip. ASME Journal of

Biomechanical Engineering 118, 399–404.

Nu *no, N., Cristofolini, L., 2001. Sensitivity analysis on the uncertain-

ties of metal-PMMA interface characteristics. In: Middleton, J.,

Jones, M.L., Shrive, N.G., Pande, G.N. (Eds.), Computer Methods

in Biomechanics and Biomedical Engineering, Vol. 3. Gordon and

Breach, London, pp. 63–68.

Nu *no, N., Amabili, M., Groppetti, R., Rossi, A., 2002. Static

coefficient of friction between Ti-6Al-4V and PMMA used in

cemented hip and knee implants. Journal of Biomedical Materials

Research 59, 191–200.

Rohlmann, A., M .o�ner, U., Bergmann, G., K .olbel, R., 1983.

Finite element analysis and experimental investigation in a

femur with hip endoprosthesis. Journal of Biomechanics 16,

727–742.

Verdonschot, N., Huiskes, R., 1996. Subsidence of THA stems due to

acrylic cement creep is extremely sensitive to interface friction.

Journal of Biomechanics 29, 1569–1575.

N. Nu *no, G. Avanzolini / Journal of Biomechanics 35 (2002) 849–852852